{"id":"https://openalex.org/W2921505209","doi":"https://doi.org/10.1155/2019/6101083","title":"Origin of Non\u2010Gaussian Velocity Distribution Found in Freestanding Graphene Membranes","display_name":"Origin of Non\u2010Gaussian Velocity Distribution Found in Freestanding Graphene Membranes","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2921505209","doi":"https://doi.org/10.1155/2019/6101083","mag":"2921505209"},"language":"en","primary_location":{"id":"doi:10.1155/2019/6101083","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/6101083","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/6101083.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2019/6101083.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055207978","display_name":"Yue Kai","orcid":"https://orcid.org/0000-0003-0785-8512"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yue Kai","raw_affiliation_strings":["School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China","School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China","institution_ids":["https://openalex.org/I116953780"]},{"raw_affiliation_string":"School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101398148","display_name":"Wenlong Xu","orcid":"https://orcid.org/0000-0002-2906-4724"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenlong Xu","raw_affiliation_strings":["School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China","School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China","institution_ids":["https://openalex.org/I116953780"]},{"raw_affiliation_string":"School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101635897","display_name":"Bailin Zheng","orcid":"https://orcid.org/0000-0001-7209-5924"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bailin Zheng","raw_affiliation_strings":["School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China","School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092"],"raw_orcid":"https://orcid.org/0000-0001-7209-5924","affiliations":[{"raw_affiliation_string":"School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China","institution_ids":["https://openalex.org/I116953780"]},{"raw_affiliation_string":"School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073314211","display_name":"Nan Yang","orcid":"https://orcid.org/0000-0002-6509-6328"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Nan Yang","raw_affiliation_strings":["School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China","School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China","institution_ids":["https://openalex.org/I116953780"]},{"raw_affiliation_string":"School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103159926","display_name":"Kai Zhang","orcid":"https://orcid.org/0000-0003-2158-8213"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kai Zhang","raw_affiliation_strings":["School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China","School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China","institution_ids":["https://openalex.org/I116953780"]},{"raw_affiliation_string":"School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047848333","display_name":"P. M. Thibado","orcid":"https://orcid.org/0000-0003-1959-1130"},"institutions":[{"id":"https://openalex.org/I78715868","display_name":"University of Arkansas at Fayetteville","ror":"https://ror.org/05jbt9m15","country_code":"US","type":"education","lineage":["https://openalex.org/I78715868"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"P. M. Thibado","raw_affiliation_strings":["Department of Physics, University of Arkansas, Fayetteville, AR 72701, USA","Department of Physics, University of Arkansas, Fayetteville, AR 72701"],"raw_orcid":"https://orcid.org/0000-0003-1959-1130","affiliations":[{"raw_affiliation_string":"Department of Physics, University of Arkansas, Fayetteville, AR 72701, USA","institution_ids":["https://openalex.org/I78715868"]},{"raw_affiliation_string":"Department of Physics, University of Arkansas, Fayetteville, AR 72701","institution_ids":["https://openalex.org/I78715868"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5047848333","https://openalex.org/A5101635897"],"corresponding_institution_ids":["https://openalex.org/I116953780","https://openalex.org/I78715868"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.4322,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.59276964,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"2019","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9890999794006348,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/graphene","display_name":"Graphene","score":0.8007544279098511},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.6444714069366455},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.6392996311187744},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.6389076709747314},{"id":"https://openalex.org/keywords/lorentz-transformation","display_name":"Lorentz transformation","score":0.6102690696716309},{"id":"https://openalex.org/keywords/membrane","display_name":"Membrane","score":0.5994237661361694},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5209330916404724},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.48014041781425476},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4174154996871948},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.3522666394710541},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3415432572364807},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.21911174058914185},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21881279349327087},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21523424983024597},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.11306950449943542},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09580177068710327}],"concepts":[{"id":"https://openalex.org/C30080830","wikidata":"https://www.wikidata.org/wiki/Q169917","display_name":"Graphene","level":2,"score":0.8007544279098511},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6444714069366455},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.6392996311187744},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.6389076709747314},{"id":"https://openalex.org/C5667645","wikidata":"https://www.wikidata.org/wiki/Q217255","display_name":"Lorentz transformation","level":2,"score":0.6102690696716309},{"id":"https://openalex.org/C41625074","wikidata":"https://www.wikidata.org/wiki/Q176088","display_name":"Membrane","level":2,"score":0.5994237661361694},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5209330916404724},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.48014041781425476},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4174154996871948},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.3522666394710541},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3415432572364807},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.21911174058914185},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21881279349327087},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21523424983024597},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.11306950449943542},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09580177068710327},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2019/6101083","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/6101083","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/6101083.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:6101083","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2019/6101083.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:b2d1c3b09c0248fcad9f9740022f0fd0","is_oa":false,"landing_page_url":"https://doaj.org/article/b2d1c3b09c0248fcad9f9740022f0fd0","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2019 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2019/6101083","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/6101083","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/6101083.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3137993762","display_name":null,"funder_award_id":"N00014-10-1-0181","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G3484348917","display_name":null,"funder_award_id":"11872280","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5150302802","display_name":null,"funder_award_id":"DMR-0855358","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320337367","display_name":"Division of Materials Research","ror":"https://ror.org/01pc7k308"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2921505209.pdf","grobid_xml":"https://content.openalex.org/works/W2921505209.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1560294171","https://openalex.org/W1970790827","https://openalex.org/W1975340316","https://openalex.org/W1975665006","https://openalex.org/W1986091197","https://openalex.org/W2011756205","https://openalex.org/W2017957151","https://openalex.org/W2030765885","https://openalex.org/W2044637056","https://openalex.org/W2059101826","https://openalex.org/W2060479771","https://openalex.org/W2076602648","https://openalex.org/W2081505615","https://openalex.org/W2089951711","https://openalex.org/W2093545327","https://openalex.org/W2098793851","https://openalex.org/W2100962665","https://openalex.org/W2137958400","https://openalex.org/W2146679582","https://openalex.org/W2493977830","https://openalex.org/W2500231823","https://openalex.org/W2520416015","https://openalex.org/W2730405628","https://openalex.org/W2767495910","https://openalex.org/W2963944687","https://openalex.org/W3029833859","https://openalex.org/W4206507589","https://openalex.org/W4249653603"],"related_works":["https://openalex.org/W2606452130","https://openalex.org/W3149465128","https://openalex.org/W3196929922","https://openalex.org/W2377562106","https://openalex.org/W3103904106","https://openalex.org/W2081887179","https://openalex.org/W4321795992","https://openalex.org/W2328592354","https://openalex.org/W3033906315","https://openalex.org/W4360593051"],"abstract_inverted_index":{"In":[0],"this":[1],"study,":[2],"an":[3],"analytic":[4],"derivation":[5],"is":[6,45,66],"made":[7],"for":[8,47,68],"the":[9,27,30,36,48,72],"truncated":[10],"Cauchy\u2010Lorentz":[11],"velocity":[12,50],"distribution":[13,51],"experimentally":[14],"observed":[15],"in":[16,52,58,78],"freestanding":[17,59],"graphene":[18,79],"membranes.":[19,80],"Three":[20],"methods":[21],"are":[22],"used":[23],"and":[24,35],"discussed,":[25],"including":[26],"Fokker\u2010Planck\u2010Kolmogorov":[28],"equation,":[29],"maximum":[31],"nonsymmetric":[32],"entropy":[33],"principle,":[34],"Bayesian":[37],"inference.":[38],"From":[39],"these":[40],"results,":[41],"a":[42,62],"physical":[43],"mechanism":[44],"provided":[46],"non\u2010Gaussian":[49],"terms":[53],"of":[54,71,75],"carbon":[55,76],"atom":[56],"arrangement":[57],"graphene.":[60],"Moreover,":[61],"new":[63],"theoretical":[64],"foundation":[65],"proposed":[67],"future":[69],"studies":[70],"anomalous":[73],"dynamics":[74],"atoms":[77]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
